How do noise-cancelling headphones use wave interference to eliminate unwanted sound?

They emit their own waves that counteract the sound-waves from the environment, thus cancelling the sound and only letting you hear your own sweet tunes.

Newton’s First Law 

Unless acted upon a large enough force, an object in motion will stay in motion. In this example, the cart moves in a more or less straight line and will do so presumably forever. However, Jaya standing in the path of the cart acts as a strong enough force to stop the cart, as her mass is greater than that of the cart.

Considerations: If there are unbalanced forces present the object will not continue in the same path of motion. Jaya stood in the way and applied a strong enough force to stop the moving cart. Even if Jaya wasn’t standing in the way, the cart would have eventually slowed down due to friction between the wheels and the floor. 

Newton’s Second Law

Newton’s Second Law is built off of the First Law. It states that the acceleration of an object due to unbalanced forces will depend directly on the unbalanced force (referred to as net force) and inversely on the mass of the body. In other words, the more mass an object has, the more net force is needed to cause it to accelerate. The formula for Newton’s Second Law is a=F/m, where F is net force, a is acceleration, and m is mass.

Considerations: There was a force of friction between the wheels and the floor. This would cause the cart to slow down quicker for each situation separately. There is also friction present between the wheels and the surface of the cart; since each cart is only supposed to support one person. This would cause the cart to slow down much quicker in the second situation. 

Newton’s Third Law 

For every action, there is an equal and opposite reaction. This can be represented by the equation F1 = F2, or m1a1 = m2a2, where F=force (N), m=mass (kg), and a=acceleration (m/s2). In this example, the cart is pushed towards the wall, which it then hits. Upon impact, the cart is pushed backwards due to the equal and opposite force being exerted from the wall.  

Considerations: In ideal conditions, this cart would rebound off the wall with the same amount of force as it hit the wall and continue going in the opposite direction forever. However, this is clearly not the case because the cart does not travel at the exact same speed directly back to the pusher. This is due to the force of friction between the wheels and the floor acting on the cart after the point of impact with the wall, and potentially the inability of the wheels to quickly change direction of rolling. Also, if the wall had any elastic properties, the cart would experience less force on the rebound become some of the initial force would be absorbed by the wall.